Nonstandard methods in option pricing

The authors use methods from nonstandard analysis to give substance to the claim that the Black-Scholes option pricing model (i.e. geometric Brownian motion) contains a built-in version of the Cox-Ross-Rubinstein model (i.e. geometric random walk). They show that the Black-Scholes model is obtained as the standard part of a hyperfinite Cox-Ross-Rubinstein model, and that objects such as contingent claims, value processes, and trading strategies are given by the standard part of the corresponding nonstandard versions. The authors present results related to the convergence of claims, value processes, trading strategies, etc. in the Cox-Ross-Rubinstein models to their continuous counterparts in the Black-Scholes model